# Mechanics of Materials, 1st edition

Published by Pearson (November 21, 2011) Â© 2012

**Paul S. Steif**

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**helps students gain physical and intuitive understanding of the ideas underlying the mechanics of materials; grasp big picture ideas; and use the subject to solve problemsâ€”everything it takes to genuinely learn how the forces acting on a material relate to its deformation and failure.**

*Mechanics of Materials*Contents

Preface viii

To the Student (pg. viii)

To the Instructor (pg. viii)

Resources for Instructors (pg. ix)

Resources for Students (pg. ix)

Acknowledgments (pg. x)

About the Author (pg. xi)

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**1. Introduction 3**

1.1 Why Study *Mechanics of Materials*? (pg. 4)

1.2 How *Mechanics of Materials *Predicts Deformation and Failure (pg. 6)

1.3 Review of Staticsâ€“Forces, Subsystems, and Free Body Diagrams (pg. 8)

1.4 Review of Staticsâ€“Representing Force Interactions Simply (pg. 10)

1.5 Review of Staticsâ€“Conditions of Equilibrium (pg. 12)

1.6 Road Map of Book (pg. 16)

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**Unit 1**

**Body Composed of Elements**

**2 Internal Force, Stress, and Strain 18**

2.1 Elements (pg. 20)

2.2 Internal Force (pg. 22)

2.3 Normal Stress (pg. 32)

2.4 Normal Strain (pg. 40)

2.5 Measuring Stress and Strain (pg. 48)

2.6 Elastic Behavior of Materials (pg. 50)

2.7 Failure and Allowable Limit on Stress (pg. 58)

2.8 Variety of Stressâ€”Strain Response (pg. 60)

2.9 Shear Strain and Shear Stress (pg. 68)

2.10 Shear and Bearing Stress in Pin Joints (pg.70)

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**Unit 2**

**Common Deformation Modes**

**3 Axial Loading 84**

3.1 Internal Forceâ€”Deformationâ€”Displacement (pg. 86)

3.2 Varying Internal Force (pg. 92)

3.3 Systems of Axially Loaded Members (pg. 100)

3.4 Statically Indeterminate Structures (pg. 108)

3.5 Thermal Effects (pg. 120)

3.6 Wrapped Cables, Rings, and Bands (pg. 128)

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**4 Torsion 136**

4.1 Rotation (pg. 138)

4.2 Shear Strain in Circular Shafts (pg. 140)

4.3 Application and Transmission of Torque (pg. 148)

4.4 Shear Stress in Circular Shafts (pg. 150)

4.5 Strength and Stiffness (pg. 162)

4.6 Dependence of Stiffness and Strength on Shaft Properties (pg. 164)

4.7 General Guidelines for Torsional Stiffness of Non-Circular Cross-Sections (pg. 166)

4.8 Torsion of Shafts with Rectangular Cross-Sections (pg. 176)

4.9 Torsion of Shafts with Thin-Walled Cross-Sections (pg. 178)

4.10 Shafts with Non-Uniform Twisting Along Their Lengths (pg. 186)

4.11 Internal Torque and the Relation to Twist and Stress (pg. 188)

4.12 Relation Between Senses and Signs of Internal Torque,Twist, and Stress (pg. 190)

4.13 Shafts with Varying Cross-Sections (pg. 192)

4.14 Statically Indeterminate Structures Subjected to Torsion (pg. 202)

4.15 Power-Torque-Speed Relations for Rotating Shafts (pg. 210)

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**5 Bending 218**

(A) Shear Forces and Bending Moments

5.1 Deformation in Bending (pg. 220)

5.2 Beams, Loads, and Supports (pg. 222)

5.3 Internal Loads in Beams (pg. 224)

5.4 Internal Loads by Isolating Segments (pg. 226)

5.5 Variation o (B) Stresses Due to Bending Moments

5.6 Strain Distribution in Bending (pg. 250)

5.7 Stresses in Bending (pg. 252)

5.8 Bending Equations (pg. 262)

5.9 Bending of Composite Cross-Sections (pg. 272)

5.10 Bending Stresses Under a Non-Uniform Bending Moment (pg. 280)

5.11 Dependence of Stiffness and Strength on Cross-Section (pg. 290)

5.12 Bending of a Beam Composed of Multiple Layers (pg. 296)

5.13 Bending of General (Non-Symmetric) Cross-Sections (pg. 298)

(C) Stresses Due to Shear Forces

5.14 Transverse Shear Stress (pg. 304)

5.15 Shear Flowâ€“Thin-Walled and Built-Up Cross-Sections (pg. 310)

(D) Deflections Due to Bending Moments

5.16 Deflections Related to Internal Loads (pg. 318)

5.17 Deflections Using Tabulated Solutions (pg. 328)

5.18 Simple Generalizations of Tabulated Solutions (pg. 332)

5.19 Complex Generalizations of Tabulated Solutions (pg. 344)

5.20 Statically Indeterminate Structures Subjected to Bending (pg. 354)

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**Unit 3**

**Design Against**

**6 Combined Loads 364**

6.1 Determining Internal Loads (pg. 366)

6.2 Drawing Stresses on 3-D Elements (pg. 372)

6.3 Pressure Vessels (pg. 380)

6.4 Elastic Stressâ€”Strain Relations (pg. 386)

6.5 Deflections Under Combined Internal Loads (pg. 392)

6.6 Strain Energy (pg. 398)

6.7 Solving Problems Using Conservation of Energy (pg. 400)

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**7 Stress Transformations and Failure 412**

7.1 Goal of Chapter, and Strain is in the Eye of the Beholder (pg. 414)

7.2 Defining Stresses on General Surfaces (pg. 416)

7.3 Stress Transformation Formulas (pg. 424)

7.4 Maximum and Minimum Stresses (pg. 432)

7.5 Mohrâ€™s Circle (pg. 440)

7.6 Failure Criteria (pg. 446)

7.7 Failure for Stresses in 3-D (pg. 454)

7.8 2-D Strain Transformations and Strain Rosettes (pg. 460)

7.9 Fatigue (pg. 466)

7.10 Stress Concentrations (pg. 468)

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**8 Buckling 480**

8.1 Buckling of Axially Loaded, Simply Supported Members (pg. 482)

8.2 Buckling of Axially Loaded Membersâ€“Alternative Support Conditions (pg. 484)

8.3 Design Equations for Axial Compression (pg. 486)

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Appendices

A. Focused Applications for Problems (pg. 501)

A-1 Bicycles (pg. 502)

A-2 Cable-Stayed Bridges (pg. 504)

A-3 Drilling (pg. 506)

A-4 Exercise Equipment (pg. 508)

A-5 Fracture Fixation (pg. 510)

A-6 Wind Turbines (pg. 512)

B. Theory of Properties of Areas (pg. 514)

B-1 Centroid and Second Moment of Inertia (pg. 514)

B-2 Products of Inertia and Principal Axes of Inertia (pg. 516)

C. Tabulated Properties of Areas (pg. 522)

D. Material Properties (pg. 525)

E. Geometric Properties of Structural Shapes (pg. 526)

F. Wood Structural Member Properties (pg. 535)

G. Tabulated Beam Deflections (pg. 536)

G-1 Deflections and Slopes of Cantilever Beams

G-2 Deflections and Slopes of Simply Supported Beams

H. Stress Concentration Factors (pg. 540)

I. Advanced Methods and Derivations (pg. 542)

I-1 Shear Stress and Twist in Thin-Walled Shaft Subjected to Torsion

I-2 Method of Singularity Functions

I-3 Derivation of Stress Transformation Formulas

I-4 Derivation of Equations for Maximum Normal and Shear Stress

Answers to Selected Problems 553

Key Terms 559

Index 561

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